Thermal expansion and thermal pressure in Co and Ni olivines: A comparison with Mn and Fe olivines

To complete the data basis for comparing the thermal behaviour of end-member olivines containing cations of the transition element series Mn (3d⁵), Fe (3d⁶), Co (3d⁷), Ni (3d⁸ subshell) the thermal expansivity of Co and Ni olivines has been studied by X-ray powder diffraction at ambient pressure and temperatures between 25 °C and 1000 °C. The anisotropy of the thermal expansion was analysed using the Kumar isothermal equation-of-state (EoS) coupled with the thermal Mie-Grüneisen EoS. For Co olivine, in order to stabilize the refinement of the EoS coefficients, our thermal expansion data were combined in a simultaneous fit with published P(a, b, c, V) and axial and bulk K^T (T) data. This reduced correlations between parameters considerably. Analogous pressure and moduli data for Ni olivine are lacking so that only unit-cell data could be fitted. The volume-related EoS coefficients of Co olivine are $K0T=$143.7(3) GPa, $K0T′=5.0(2)$⁠, $γ0MG=1.23(1)$⁠, $V0=295.69(5)$ Å³ with the acoustic Debye temperature fixed at 551 K. Axial expansivities α are controlled by compressibilities β_T and thermal pressures (∂P/∂T)_V according to α = β_T (∂P/∂T)_V. For olivines, the structural features suggest a sequence of compressibilities with β_T,b > β_T,c > β_T,a (SG Pbnm). Usually, a similar ranking is also found for the axial expansivities. In the case of olivines, however, only Mn olivine meets the expectation, contrary to Fe olivine and to a lesser extent to Co and Ni olivine. The reason for the unusual behaviour is found in the specific anisotropies of the axial thermal pressures. Extrapolation of thermal expansivities and of linear and bulk moduli is justified up to 2200 K, judged from the fulfillment of the relations $1/K VT=1/3K aT+1/3K bT+1/3K cT$ and $αV(T)=αa(T)+αb(T)+αc(T)$⁠.